principal submatrix (english) - meaning, definition, translation, pronunciation

Part of Speech

Noun

Phonetic Transcription

/prɪnˈsɪp.əl ˈsʌbˌmæt.rɪks/

Meaning and Usage

A principal submatrix refers to a submatrix that is formed from a square matrix by selecting rows and columns that correspond to the same indices (usually the first k rows and first k columns of an n x n matrix). It is often used in linear algebra, statistics, and various applied mathematics fields. The term is more frequently used in written contexts, especially in mathematical texts, research papers, and academic discussions.

Example Sentences

1. The study analyzed the properties of the principal submatrix and its impact on the overall determinant.

2. Translation: El estudio analizó las propiedades de la submatriz principal y su impacto en el determinante total.

3. To find the eigenvalues of the matrix, we first computed the principal submatrix by eliminating the last row and column.

4. Translation: Para encontrar los valores propios de la matriz, primero calculamos la submatriz principal eliminando la última fila y columna.

5. The principal submatrix can provide significant insights into the behavior of the full matrix.

6. Translation: La submatriz principal puede proporcionar información significativa sobre el comportamiento de la matriz completa.

Idiomatic Expressions

While "principal submatrix" is a technical term primarily used in mathematics, it doesn't appear often in idiomatic expressions. However, the word "principal" may show up in various idiomatic contexts:

1. Principal player: He was the principal player in the success of the project.

2. Translation: Él fue el jugador principal en el éxito del proyecto.

3. Principal concern: My principal concern is the safety of the team.

4. Translation: Mi preocupación principal es la seguridad del equipo.

5. Principal reason: The principal reason for the failure was lack of funding.

6. Translation: La razón principal del fracaso fue la falta de financiación.

7. Principal aim: The principal aim of the research is to improve efficiency.

8. Translation: El objetivo principal de la investigación es mejorar la eficiencia.

Etymology

The term principal comes from the Latin word "principalis," which means "chief" or "foremost." Meanwhile, submatrix is derived from the combination of the prefix "sub-", meaning "under" or "below," and "matrix," which comes from Latin "matrix," meaning "womb" or "source." Together, they denote a "smaller matrix" derived from a "main" or "larger" matrix.

Synonyms and Antonyms

Synonyms: - Minor submatrix - Reduced matrix

Antonyms: - Complete matrix - Full matrix

This comprehensive overview of “principal submatrix” presents its usage, meaning, and related information effectively for further understanding.